The HS2 rail project has an estimated £3.3bn funding gap which the Government has yet to decide how to fill, a new report says.

It was also not clear how HS2 high-speed rail scheme, which is bitterly opposed in some quarters, would deliver and rebalance economic growth, the report by the National Audit Office (NAO) added.

The timetable for planning phase one of the project – from London to Birmingham with work due to start in 2016/17 – was "challenging", the NAO said, and "makes delivering this work difficult and increases the risk that the programme will have a weak foundation for securing and demonstrating success in the future”.

Expressing "reservations" about the business case for HS2, the NAO said the Department for Transport's (DfT) methodology for appraising the project put a high emphasis on journey-time savings, from faster and more reliable journeys.

But the report added that the relationship between these savings and the strategic reasons for doing the project, such as rebalancing regional economies, was unclear.

The NAO said it was also unclear whether the business case covered just phase one or the full route including phase two – the Y-shaped network from Birmingham to Manchester and Leeds due to open in 2032/33.

The report said phase two had a strong economic case but that this was much less certain as route designs were less well-developed.

Saying there were "risks to affordability", the NAO went on: "The NAO estimates that there is a £3.3bn funding gap over four years (2017-18 to 2020-21) which the government has yet to decide how to fill."

The report said this "gap in affordability" coincided with the "peak spending years for phase one".

The NAO continued: "The department capital forecast for these four years is £33.7bn but its capital budget if kept constant at 2014-15 levels would be only £30.4bn."

The NAO said the benefit-cost ratio – the cost of the project set against the likely benefits it will bring – had twice contained errors and that the current estimate of £1.40 in benefit to every £1 spent was "likely to change".

It added that between March 2010 and February 2011 benefits from HS2 reduced by £12bn, with nearly two-thirds of this reduction due to errors in the way passenger demand was modelled.

The report said that the DfT estimated the line would support 100,000 jobs through development around stations in constructing and operating the line.

The report went on: "It (the DfT) does not know how many jobs would be created without this investment."

The NAO also said that HS2 Ltd had not yet analysed the effect of premium pricing on forecast passenger demand, revenues and the benefit-cost ratio.

The report went on: "To forecast passenger demand, HS2 Ltd uses the same average fares for high-speed and conventional rail in its models, although premium fares are charged for HS1 (the London to Folkestone Channel Tunnel link)".

"It's too early in the HS2 programme to conclude on the likelihood of its achieving value for money. Our concern at this point is the lack of clarity around the department's (DfT) objectives," says NAO head Amyas Morse.

"The strategic case for the network should be better developed at this stage of the programme. It is intended to demonstrate the need for the line but so far presents limited evidence on forecast passenger demand and expected capacity shortages on existing lines.

"It is also unclear how HS2 will transform regional economies by delivering jobs and growth.

"The department is trying against a challenging timetable to strengthen its evidence and analysis, which at present provide a weak foundation for securing and demonstrating success in the programme in future."

Commenting on the report, House of Commons Public Accounts Committee chairman Margaret Hodge says: "The DfT has produced a business case that is clearly not up to scratch and shows no signs of having learnt the lessons from HS1, which the committee reported on last year. "

She continues: "Some of their (the DfT's) assumptions are just ludicrous. To take just one example, on the benefits to business travellers, the department continues to assume that business travellers do not work when on the train and to use data that is over 10 years old.

"HS1 ended up costing the taxpayer billions when it was supposed to pay for itself. An estimated £3bn funding gap has been identified for HS2, already bringing into question the affordability of this project."

Hodge continued: "There is virtually no evidence in this business case to support claims that HS2 will deliver regional economic growth, one of the key aims and justifications for this project.

"We have been told that it will deliver around 100,000 new jobs but there is no evidence that all these jobs would not have been created anyway. The department has also set an extremely ambitious timetable for the project, with no room for mistakes. Past experience does not fill us with confidence in this optimism.

"Unless the department gets its act together, HS2 will not deliver all intended benefits for travellers and the regions, and it will not deliver value for the taxpayer.”

Transport Secretary Patrick McLoughlin said: "I welcome any examination of the HS2 programme, but I do not accept the NAO's core conclusion. This is because it depends too much on out-of-date analysis and does not give due weight to the good progress that has been made since last year.

"This includes the appointment of an expert management team and the announcement of detailed plans for the line north of Birmingham."

He added: "The case for HS2 is clear. Without it the key rail routes connecting London, the Midlands and northern England will be overwhelmed. HS2 will provide the capacity needed in a way that will generate hundreds of thousands of jobs and billions of pounds worth of economic benefits.

"Economic modelling is just the start of the story. If we only relied on modelling we would not have built the M1, parts of the M25 or the (Tube's) Jubilee line extension to Canary Wharf.

"We are not building HS2 simply because the computer says 'yes'. We are building it because it is the right thing to do to make Britain a stronger and more prosperous place."

On the £3.3bn gap in affordability, the DfT said: "We do not recognise the funding gap that the NAO quotes."

Chris Richards, Transport Policy Advisor at the Institution of Engineering and Technology said: “In our response to the Department for Transport consultation we made it clear that there were potential flaws in the analysis, several assumptions were made in crucial areas and serious questions have been left unanswered.

“HS2 is a project of major national significance, if we get this wrong, we will regret it for decades to come.”